U.S. patent application number 15/375479 was filed with the patent office on 2017-03-30 for continously variable transmission.
The applicant listed for this patent is Abbas Olyaei. Invention is credited to Abbas Olyaei.
Application Number | 20170089428 15/375479 |
Document ID | / |
Family ID | 58408635 |
Filed Date | 2017-03-30 |
United States Patent
Application |
20170089428 |
Kind Code |
A1 |
Olyaei; Abbas |
March 30, 2017 |
CONTINOUSLY VARIABLE TRANSMISSION
Abstract
In a continuously variable transmission (CVT) system, an input
shaft receives power from an external source and rotates an
intermediate mechanism that converts the rotation to an oscillatory
movement and converts the oscillatory movement to a one-way
rotation that drives an output shaft, with transmission ratio
according to load on the output shaft.
Inventors: |
Olyaei; Abbas; (Marand,
IR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Olyaei; Abbas |
Marand |
|
IR |
|
|
Family ID: |
58408635 |
Appl. No.: |
15/375479 |
Filed: |
December 12, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62265462 |
Dec 10, 2015 |
|
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|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
F16H 29/22 20130101 |
International
Class: |
F16H 3/44 20060101
F16H003/44 |
Claims
1. A transmission system configured to deliver power with a
variable transmission ratio, comprising: an input shaft configured
to receive power from an external power source, having two pinions,
mounted at respective opposite ends of the input shaft, and
rotatable therewith; two rotating members, each rotatably mounted
on a respective one of two mounting members opposite one another,
each rotating member having a gear mounted thereon and rotatable
therewith, each gear configured to mesh with the respective pinion
on the input shaft and receive power therefrom; two radial rails,
each radial rail mounted radially on a corresponding one of the two
rotating members and configured to be rotatable therewith; a free
shaft configured to be slidably coupled to the sliding rails at
either ends thereof; and a plurality of follower assemblies mounted
around the free shaft, each follower assembly comprising: a
follower shaft rotatably mounted between the mounting members
parallel to the free shaft with a one-way bearing unit coupled
thereon at one end thereof; and a slotted link having a proximal
end pivotally mounted on the follower shaft and a slot configured
to engage with the free shaft configured to facilitate a reciprocal
linear movement of the free shaft therein; a planetary gear system
having a plurality of planet gears mounted on the respective
follower shafts, the planet gears arranged around a sun gear and
mesh therewith; each planet gear mounted on the respective one-way
bearing unit on the respective follower shaft and configured to
transfer the rotational movement of the follower shaft to the sun
gear; and an output shaft with the sun gear mounted thereon and
rotatable therewith, configured to deliver the power received via
the sun gear; wherein, the free shaft and the plurality of slotted
links engaged therewith are configured to transform the rotational
movement of the rotating members into an oscillatory movement of
the slotted links with a variable amplitude; wherein, the plurality
of the follower shafts and the planet gears mounted thereon are
configured to transform the oscillatory movement of the slotted
links into the rotational movement of the sun gear; and wherein,
the variable transmission ratio between the input shaft and the
output shaft is a function of the variable amplitude of the
oscillatory movement of the slotted links.
2. The transmission system according to claim 1, wherein the free
shaft is slidably movable on the radial rails in a sliding path
from the center of the rotating members to an outer point on the
perimeter of the rotating members.
3. The transmission system according to claim 1, wherein the
plurality of the follower assemblies include at least two follower
assemblies.
4. The transmission system according to claim 1, wherein the
plurality of the planet gears include at least two planet
gears.
5. The transmission system according to claim 1, further comprising
a clutch mounted between the sun gear and the output shaft.
6. The transmission system according to claim 5, wherein the clutch
is a spring clutch, and is configured to compensate output velocity
fluctuations induced as a result of the oscillatory movements of
the follower assemblies.
7. A method for delivering power with a variable transmission
ratio, comprising rotating a rotatable input shaft with an external
power; rotatably driving two rotatable members with the rotatable
input shaft, the rotatable members being supported to rotate on a
shared center axis and spaced apart along the shared center axis;
converting the rotating of the two rotatable members to an
oscillatory movement of each of a plurality of slotted links,
wherein converting the oscillatory movement of each of the
plurality of slotted links is configured with a variable amplitude
of the oscillatory movement; converting the oscillatory movement of
each of the plurality of slotted links to a one-way rotation of a
corresponding planetary gear among a plurality of planetary gears,
wherein a ratio of the rotations of each of the two rotatable
members to rotations of the corresponding planetary gear is
dependent on the amplitude of the oscillatory movement; driving a
sun gear, coupled to an output shaft driving a resistance, with the
one-way rotation of each of the plurality of planetary gears; and
varying the amplitude of the oscillatory movement in response to a
varying of the resistance driven by the output shaft.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of priority from pending
U.S. Provisional Patent Application No. 62/265,462, filed on Dec.
10, 2015, and entitled "CONTINUOUSLY VARIABLE TRANSMISSION," which
is incorporated herein by reference in its entirety.
TECHNICAL FIELD
[0002] The present disclosure generally relates to a transmission
system, and more particularly to a continuously variable
transmission (CVT) system.
BACKGROUND
[0003] A continuously variable transmission (CVT), also known as a
single-speed transmission, step-less transmission, or, in case of
motorcycles, a twist-and-go, is an automatic transmission that can
change the ratio of power transmission uniformly through a
continuous range of effective gear ratios. Unlike mechanical
transmissions that offer a fixed number of gear ratios, a CVT is
not restricted to a finite number of ratios, capable of providing
an infinite number of gear ratios. A CVT may be used in a wide
variety of applications including automobiles, recreational
vehicles, turbines and industrial equipment. There is a need in the
art for CVT systems with lower power losses due to friction, and
without a need for complex control systems.
SUMMARY
[0004] The following brief summary is not intended to include all
features and aspects of the present application, nor does it imply
that the application must include all features and aspects
discussed in this summary.
[0005] Various exemplary apparatuses are disclosed, and examples
may include a transmission system that may be configured to deliver
power with a variable transmission ratio. The transmission system
may include: an input shaft that may be configured for receiving
power from an external power source, having two pinions mounted at
either ends thereof and rotatable therewith; two rotating members
that may be rotatably mounted opposite one another, each may have a
gear mounted thereon and rotatable therewith, each gear may be
configured to mesh with the respective pinion on the input shaft
and receive power therefrom; two radial rails that may be mounted
radially on each rotating member and may be configured to be
rotatable therewith; a free shaft that may have two sliding members
that may be attached thereto at either ends thereof, each sliding
member may be configured to surround and be slidably coupled to the
respective sliding rail and thereby slidably couple the free shaft
with the sliding rails at either ends thereof; and a plurality of
follower assemblies that may be mounted around the free shaft. Each
follower assembly may include: a follower shaft that may be
rotatably mounted parallel to the free shaft with a one-way bearing
unit coupled thereon at one end thereof; and a slotted link that
may have a proximal end that may be pivotally mounted on the
follower shaft and a slot that may be configured to engage with the
free shaft which may facilitate a reciprocal linear movement of the
free shaft therein; a planetary gear system that may have a
plurality of planet gears that can be mounted on the respective
follower shafts, the planet gears may be arranged around a sun gear
and mesh therewith; each planet gear may be mounted on the
respective one-way bearing unit on the respective follower shaft
and may be configured to transfer the rotational movement of the
follower shaft to the sun gear; and an output shaft with the sun
gear mounted thereon and rotatable therewith that may be configured
to deliver the power received via the sun gear.
[0006] In an aspect, the free shaft and the plurality of slotted
links engaged therewith may be configured to transform the
rotational movement of the rotating members into the oscillatory
movement of the slotted links with a variable amplitude. The
plurality of the follower shafts and the planet gears mounted
thereon may be configured to transform the oscillatory movement of
the slotted links into the rotational movement of the sun gear and
the variable transmission ratio between the input shaft and the
output shaft may be a function of the variable amplitude of the
oscillatory movement of the slotted links.
[0007] In one implementation, the free shaft may be slidably
movable on the radial rails in a sliding path from the center of
the rotating members to an outer point on the perimeter of the
rotating members.
[0008] In another implementation, the plurality of the follower
assemblies may include at least two follower assemblies. The
plurality of the planet gears may include at least two planet
gears.
[0009] According to another implementation, the transmission system
may further include a clutch mounted between the sun gear and the
output shaft. In an aspect the clutch can be a spring clutch, and
may be configured to compensate output velocity fluctuations
induced as a result of the oscillatory movements of the follower
assemblies.
[0010] Disclosed methods include delivering power with a variable
transmission ratio, and can include rotating a rotatable input
shaft with an external power, and rotatably driving two rotatable
members with the rotatable input shaft, where the rotatable member
can be supported to rotate on a shared center axis and spaced apart
along the shared center axis. Example methods delivering power with
a variable transmission ratio can also include converting the
rotating of the two rotatable members to an oscillatory movement of
each of a plurality of slotted links and, in an aspect, converting
the oscillatory movement of each of the plurality of slotted links
can be configured with a variable amplitude of the oscillatory
movement. Example methods for delivering power with a variable
transmission ratio can also include converting the oscillatory
movement of each of the plurality of slotted links to a one-way
rotation of a corresponding planetary gear among a plurality of
planetary gears and, in an implementation, a ratio of the rotations
of the two rotatable members to rotations of the corresponding
planetary gear can be dependent on the amplitude of the oscillatory
movement. Example methods for delivering power with a variable
transmission ratio can also include driving a sun gear, coupled to
an output shaft driving a resistance, with the one-way rotation of
each of the plurality of planetary gears, and can include varying
the amplitude of the oscillatory movement in response to a varying
of the resistance driven by the output shaft.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] While the specification concludes with claims particularly
pointing out and distinctly claiming the subject matter that is
regarded as forming the present application, it is believed that
the application will be better understood from the following
description taken in conjunction with the accompanying DRAWINGS,
where like reference numerals designate like structural and other
elements, in which:
[0012] FIG. 1A illustrates an example implementation of the CVT
system with four follower assemblies, according to one or more
aspects of the present disclosure.
[0013] FIG. 1B illustrates an example implementation of the CVT
system with two follower assemblies, according to one or more
aspects of the present disclosure.
[0014] FIG. 2A illustrates a top view of an exemplary rotating
guide subsystem, according to one or more aspects of the present
disclosure.
[0015] FIG. 2B is a perspective view of an exemplary rotating guide
assembly, according to one or more aspects of the present
disclosure.
[0016] FIG. 3A is a perspective view of an exemplary follower
assembly, according to one or more aspects of the present
disclosure.
[0017] FIG. 3B illustrate two example implementations of a slotted
link, according to one or more aspects of the present
disclosure.
[0018] FIGS. 4A and 4B are front views of a follower assembly and a
free shaft engaged therewith, according to one or more aspects of
the present disclosure.
[0019] FIGS. 5A and 5B illustrate top views of an exemplary
rotating guide subsystem, according to one or more aspects of the
present disclosure.
[0020] FIG. 6 illustrates a front view of a slotted link engaged
with a free shaft on a rotating guide assembly, according to one or
more aspects of the present disclosure.
DETAILED DESCRIPTION
[0021] In the following detailed description, numerous specific
details are set forth by way of examples in order to provide a
thorough understanding of the relevant teachings. However, it
should be apparent that the present teachings may be practiced
without such details. In other instances, well known methods,
procedures, components, and/or circuitry have been described at a
relatively high-level, without detail, in order to avoid
unnecessarily obscuring aspects of the present teachings.
[0022] For purposes of explanation, specific nomenclature is set
forth to provide a thorough understanding of exemplary embodiment
of the present disclosure. However, it will be apparent to those
skilled in the art that these specific details are not required to
practice exemplary embodiments of the present disclosure.
Descriptions of specific applications are provided only as
representative examples. Various modifications to the exemplary
implementations may be readily apparent to one skilled in the art,
and the general principles defined herein may be applied to other
implementations and applications without departing from the
principles of the exemplar embodiment of the present disclosure.
Practices according to concepts disclosed by the present disclosure
are not intended to be limited to the implementations shown, are to
be accorded the widest possible scope consistent with the
principles and features disclosed herein.
[0023] Disclosed systems and apparatuses are directed to a
self-adjustable CVT that may be configured for delivering power
from an input shaft with a continuously variable transmission ratio
to an output shaft. The power may be received from an external
power source via the input shaft, and the input shaft may be
coupled with and drive a rotational movement of an intermediate
mechanism, which may be configured to transmit the power received
from the input shaft to a planetary gear system with a continuously
variable transmission ratio. In an aspect, the intermediate
mechanism may be configured to transform the rotational movement of
the input shaft into an oscillatory movement with a continuously
adjustable amplitude and then convert this oscillatory movement to
the rotational movement of the output shaft via the planetary gear
set, thereby adjusting the transmission ratio needed in the output.
In other words, the input power may be transmitted to the output
shaft with a transmission ratio adjusted based on the amplitude of
the oscillatory movement of the intermediate mechanism.
[0024] FIGS. 1A and 1B show perspective views of examples of the
CVT system, according to one or more aspects of the present
disclosure. Referring to FIGS. 1A and 1B, the exemplary CVT system
100 may include two spaced apart mounting members 102 and 102' (not
visible in FIG. 1A) that may provide mounting means for mounting
different parts of the CVT system 100; an input shaft 101 that may
be configured to receive power from an external power source; an
intermediate mechanism 103 that may be configured to continuously
adjust the transmission ratio; a planetary gear set 104 that may be
configured to receive the power from the intermediate mechanism 103
with the adjusted transmission ratio; and an output shaft 105 that
may be coupled with the planetary gear set 104 and may be
configured to deliver the power received from the planetary gear
set 104 to an external consumer.
[0025] Referring to FIGS. 1A and 1B, the intermediate mechanism 103
may include two rotating members 110 and 110' that may be rotatably
mounted opposite from one another on two rotating shafts 111
(visible and numbered in FIG. 2A) that pass through each mounting
member 102 and 102'. The rotational axes of the rotating members
110 and 110' may be aligned with a central axis 118 of the CVT
system 100. The input shaft 101 may be coupled with and drive the
rotational movement of the rotating members 110 and 110' about the
axis 118 via two gear-pinion sets 106 and 106' at either sides of
the CVT system 100. The gear-pinion sets 106 and 106' may include
two pinions 107 and 107' that may be coaxially mounted on the input
shaft 101 at either sides of the CVT system 100; and two gears 108
and 108' that may be respectively mounted on the rotating shafts
111 (visible and numbered in FIG. 2A) and may be configured to mesh
with corresponding pinions 107 and 107'. The power transmitted form
the input shaft 101 via gear-pinion sets 106 and 106' to rotating
members 110 and 110' may drive the rotational movement of the
rotating members 110 and 110' about the central axis 118. Two
parallel radial rails 113 and 113' may be radially mounted on
respective rotating members 110 and 110'. Referring to the
implementation shown in FIG. 2A, radial rail 113 may be radially
mounted on the rotating member 110 using two mounting members 201
and radial rail 113' may be radially mounted on the rotating member
110' using two mounting segments 201'.
[0026] Referring to FIGS. 1A, 1B and 2A, the intermediate mechanism
103 may include a free shaft 109 slidably mounted between the two
rotating members 110 and 110'. Referring to FIG. 2A, the free shaft
109 may have two sliding segments 114 and 114' that may be formed
on either ends of the free shaft 109 and may be configured to
surround, and be slidably movable along radial rails 113 and 113'.
As a result, the two radial rails 113 and 113' define a sliding
track for the free shaft 109 and the free shaft may radially slide
along the track formed by the parallel radial rails 113 and 113'
back and forth in the direction shown by arrow 202. In an
implementation, a restoring spring 120 may be utilized at the
distal end of each sliding rails 113 and 113' that may be
configured to restore the position of the free shaft 109 towards
the central axis 118, as will be described in more detail in
connection with FIGS. 5A and 5B later in this disclosure.
[0027] Referring to FIGS. 2A and 2B, the sliding rails 113 and 113'
may be configured as stepped bars with two different cross sections
defining a sliding path 117 for the free shaft 109. The proximal
end of the sliding path 117 may be near the central axis 118 of the
rotating members 110, 110' and distal end of the sliding path 117
may be near their perimeters. In an implementation, a restoring
spring 120 may be utilized at the distal end of the sliding path
117 that may be configured to restore the position of the free
shaft 109 towards the central axis 118, as will be described in
more detail later in this disclosure. Referring to the
implementation shown in FIG. 2A, the rotating members 110, 110' may
be rotatably coupled with gears 108 and 108' via coupling members
111.
[0028] Referring to FIG. 1B, the intermediate mechanism 103 may
further include a number of follower assemblies 121, for example
two follower assemblies 121 as shown in FIG. 1B or four follower
assemblies (not explicitly numbered) as shown in FIG. 1A.
[0029] FIG. 3A illustrates an example of a follower assembly 121
that may include a slotted link 122, and a follower shaft 123. The
proximal end of the slotted link 122 may be configured with a
connecting segment 124 that may be configured to tightly surround
and thereby be pivotally mounted on the follower shaft 123 without
any unwanted sliding movements relative to the follower shaft 123.
The slotted link 122 may pivot about the longitudinal axis 128 of
the follower shaft 123. The slotted link 122 may be configured with
a slot 125 through which, the free shaft 109 can be engaged with
the slotted link 122. The free shaft 109 may have a free
reciprocating linear movement along the slot 125. Referring to FIG.
3, the slotted link may be configured with a straight shape 130 or
a curved shape 131.
[0030] Referring to FIGS. 1A and 1B, the free shaft 109 may pass
through all slotted links 122. The rotational movement of the
rotating members 110, 110' cause the rotational movement of the
free shaft 109 about the axis 118 in a rotational path with a
radius that may be defined by the radial distance of the free shaft
109 relative to the axis 118. The rotation of the free shaft 109
about axis 118 may cause an oscillating movement in the slotted
links 122 about their pivot points. The position of the free shaft
109 on the radial rails 113 and 113' decides the amplitude of the
oscillating movement of the slotted links 122. The further the free
shaft 109 is away from the central axis 118, the larger is the
amplitude of the oscillating movement of the slotted links 122.
[0031] Referring to FIG. 3A, the oscillating movement of the
slotted link 122 about the pivot point defined by the connecting
ring 124 drives a back and forth rotational movement of the
follower shaft 123 about its longitudinal axis 128 in a direction
shown by arrow 301.
[0032] Referring to FIGS. 1A and 1B, planetary gear set 104 may
include a number of planet gears arranged around a sun gear. The
number of planet gears may be equal to the number of follower
assemblies. Referring to FIG. 3A, the planet gear 127 may be
coupled at one end of the follower shaft 123 on a one-way bearing
unit 126. The one-way bearing unit 126 may limit the rotation of
the planet gear 127 to be in one direction. For example, when the
follower shaft 123 rotates back and forth as shown by arrow 301,
due to the presence of the one-way bearing unit 126, the planet
gear rotates in one direction shown by arrow 302.
[0033] Referring to FIGS. 1A and 1B, the follower shafts 123 may
drive the rotational movement of the planet gears 127. The planet
gears 127 may be configured to mesh with the sun gear 129 and drive
the rotational movement thereof. The one-way rotational movements
of the planet gears 127 are transformed by the sun gear 129 into a
uniform rotational movement of the output shaft 105. In some
implementations, a clutch 132 may connect the sun gear 129 to the
output shaft 105, in order to adjust the rotation of the sun gear
129 with the output shaft 105 without any power shock. The output
shaft 105 may be coupled with external power consumers and may
transmit power with a desired torque and rotational speed according
to the load demands.
[0034] As the load on the output shaft 105 increases, the planet
gears 127 must transmit more power, as a result, the follower
assemblies 121 must oscillate with higher amplitudes, and
therefore, the slotted links 122 urge the free shaft 109 to move
towards larger radial distances from the central axis 118 and
thereby the transmission ratio increases.
[0035] FIG. 4A shows an example of how the rotational movement of
the rotating members may be transformed into the oscillating
movements of the follower assemblies and how the radius of rotation
of the free shaft about the central axis determines the amplitude
of the oscillatory movement of each follower assembly. In the
example shown in FIG. 4A, the free shaft 109 is positioned on the
radial rails 113 and 113' (visible in FIG. 2B) close to the central
axis 118. As the free shaft 109 rotates about the central axis 118
with a radius 401 in the direction shown by arrow 402, the slotted
link 122 is urged to pivot about the longitudinal axis of the
follower shaft 123 from an initial position 403 to a secondary
position 404 and thereby rotates the planet gear 127 in the
direction shown by arrow 405. Referring to FIG. 4A, as the free
shaft 109 rotates back to its initial position in the direction
shown by arrow 406, the slotted link 122 rotates clockwise form the
secondary position 404 to the initial position 403, since a one-way
bearing unit 126 is used to couple the follower shaft 123 with the
planet gear 127, the planet gear 127 does not rotate when the
slotted link 122 goes back to its initial position in the direction
shown by arrow 406. As the free shaft 109 rotates in the direction
shown by arrow 402, the slotted link 122 oscillates as shown by
arrow 407.
[0036] FIG. 4B shows an example of how the transmission ratio is
self-adjusted when the load on the output changes. In this example,
the output load has increased compared to the situation shown in
FIG. 4A. An increase in the output load requires an increase in the
output power, which means the planet gear 127 must deliver more
power. To this end, the slotted link 122 must oscillate with higher
amplitudes in order to be able to deliver higher powers. As a
higher amplitude is needed for the slotted link 122, the free shaft
109 is urged to slide on the radial rails 113 and 113' (visible in
FIG. 2B) along the sliding path 117 (visible in FIG. 2B) towards a
higher radius 408. In this case the slotted link 122 oscillates as
shown by arrow 407 with a higher amplitude compared to the example
shown in FIG. 4A.
[0037] Referring to FIGS. 1A and 1B, the clutch 132 may be a spring
clutch, which may be considered as a cylinder that may be connected
to the output shaft 105 with a spring. The spring clutch 132 may
cover the gap between the power transmitted by different follower
assemblies due to their different operational phases, as was
described in detail in connection with FIGS. 4A and 4B compensating
the output velocity fluctuations induced as a result of the
oscillatory movements of the intermediate mechanism 103, as well as
giving the CVT 100 enough freedom to rotate slightly and get
adjusted in sudden transmission ratio changes, such as in sudden
break situations.
[0038] Referring to the FIG. 4A, the oscillating movement of
slotted link 122 is a function of the corresponding contact point
409 at which the free shaft 109 is engaged with the slot 410 of the
slotted link 122. A straight relation exists between the rotational
speed of the output shaft and the amplitude of the oscillating
movement of slotted link 122. As the free shaft 109 slides on the
radial rails toward higher radiuses from the central axis 118, the
amplitude of the oscillating movement of slotted link 122
increases, therefore the corresponding planet gear 127 mounted on
the corresponding follower shaft 123 rotates faster and produces
higher gear ratios. If output loading condition is in a way that
the output shaft is limited to rotate in a specific velocity, it
forces the follower assemblies to reduce their oscillation
amplitude, and in turn the follower forces the free shaft 109 back
to the smaller radiuses.
Calculation of Transmission Ratio
[0039] FIG. 5A shows the position of the free shaft 109 on the
radial rails 113 and 113' with a minimum distance (.DELTA..sub.min)
between the center of the free shaft 501 and the central axis 118
corresponding to a minimum transmission ratio. FIG. 5B shows the
position of the free shaft 109 on the radial rails 113 and 113'
with a maximum distance (.DELTA..sub.max) between the center of the
free shaft 501 and the central axis 118 corresponding to a maximum
transmission ratio. The minimum value of .DELTA. may reach to very
small amounts but it must be a little greater than zero
(.DELTA.>0), in order for CVT to start working. Because in the
case of .DELTA.=0 the CVT cannot start to change .DELTA. with the
help of centrifugal force due to the rotation.
[0040] FIG. 6 illustrates one example of a slotted link 601 in two
different positions 601, 602. The radial distance between central
axis of the follower shaft 606 and the central axis of the radial
sliding rail 604 is represented as R.sub.0; the radial distance
between the central axis of the radial sliding rail 604 and the
central axis of the free shaft 605 is represented by .DELTA.; input
angular velocity is represented by .omega..sub.i; and angular
velocity of the follower shaft 123 is represented by .omega..sub.o;
Parameter ".alpha.", the angular position of radial sliding rail
604 with respect to the horizontal direction, is free to change its
value from zero to 2.pi. as the free shaft 605 oscillates. The
angle of slotted link 601 designated as ".beta." with respect to
horizontal direction is a function of .alpha.. This functionality
can be expressed by Equation (1) below, as:
tan ( .beta. ) = .DELTA.sin ( .alpha. ) R 0 - .DELTA.cos ( .alpha.
) Equation ( 1 ) ##EQU00001##
[0041] For
- .pi. 2 < .alpha. < .pi. 2 ##EQU00002##
the transmission ratio may be expressed by Equation (2) below
as
R = .omega. o .omega. i = .DELTA. R 0 - .DELTA. Equation ( 2 )
##EQU00003##
while for
.pi. 2 < .alpha. < 3 .pi. 2 ##EQU00004##
the transmission ratio can be described by Equation (3) below
as:
R = .omega. o .omega. i = .DELTA. R 0 + .DELTA. Equation ( 3 )
##EQU00005##
[0042] .beta. can take all values, maximum .beta. is achieved at
.alpha.=.pi./2 with a magnitude that can be expresses as Equation
(4) below as
tan ( .beta. max ) = .DELTA. R 0 Equation ( 4 ) ##EQU00006##
[0043] While the foregoing has described what are considered to be
the exemplary embodiments, it is understood that various
modifications may be made therein and that the subject matter
disclosed herein may be implemented in various forms and examples,
and that the teachings may be applied in numerous applications,
only some of which have been described herein. It is intended by
the following claims to claim any and all applications,
modifications and variations that fall within the true scope of
exemplary embodiments consistent with the present disclosure.
[0044] It will be understood that the terms and expressions used
herein have the ordinary meaning as is accorded to such terms and
expressions with respect to their corresponding respective areas of
inquiry and study except where specific meanings have otherwise
been set forth herein. Relational terms such as first and second
and the like may be used solely to distinguish one entity or action
from another without necessarily requiring or implying any actual
such relationship or order between such entities or actions. The
terms "comprises," "comprising," or any other variation thereof,
are intended to cover a non-exclusive inclusion, such that a
process, method, article, or apparatus that comprises a list of
elements does not include only those elements but may include other
elements not expressly listed or inherent to such process, method,
article, or apparatus. An element proceeded by "a" or "an" does
not, without further constraints, preclude the existence of
additional identical elements in the process, method, article, or
apparatus that comprises the element.
* * * * *